On contact surgery and knot Floer invariants

Abstract

We establish some general relations between Heegaard Floer based contact invariants. In particular, we observe that if the contact invariant of large negative, respectively positive, contact surgeries along a Legendrian knot does not vanish, then the Legendrian invariant, respectively the Legendrian inverse limit invariant, of that knot is non-zero. We use sutured Floer homology, and the limit constructions due to Golla, and Etnyre, Vela-Vick and Zarev.